8v^2+6v-27=0

Solution for 8v^2+6v-27=0 equation:

Simplifying
8v2 + 6v + -27 = 0

Reorder the terms:
-27 + 6v + 8v2 = 0

Solving
-27 + 6v + 8v2 = 0

Solving for variable 'v'.

Factor a trinomial.
(-9 + -4v)(3 + -2v) = 0

Subproblem 1
Set the factor '(-9 + -4v)' equal to zero and attempt to solve:

Simplifying
-9 + -4v = 0

Solving
-9 + -4v = 0

Move all terms containing v to the left, all other terms to the right.

Add '9' to each side of the equation.
-9 + 9 + -4v = 0 + 9

Combine like terms: -9 + 9 = 0
0 + -4v = 0 + 9
-4v = 0 + 9

Combine like terms: 0 + 9 = 9
-4v = 9

Divide each side by '-4'.
v = -2.25

Simplifying
v = -2.25
Subproblem 2
Set the factor '(3 + -2v)' equal to zero and attempt to solve:

Simplifying
3 + -2v = 0

Solving
3 + -2v = 0

Move all terms containing v to the left, all other terms to the right.

Add '-3' to each side of the equation.
3 + -3 + -2v = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -2v = 0 + -3
-2v = 0 + -3

Combine like terms: 0 + -3 = -3
-2v = -3

Divide each side by '-2'.
v = 1.5

Simplifying
v = 1.5
Solution
v = {-2.25, 1.5}